{"type":"ScholarlyArticle","title":"A Random Model for Argumentation Framework: Phase Transitions, Empirical Hardness, and Heuristics","authors":[{"name":"Yong Gao","slug":"yong-gao","given":"Yong","family":"Gao","affiliation":"Department of Computer Science , University of British Columbia Okanagan , Kelowna , Canada"}],"abstract":"We propose and study, theoretically and empirically, a new random model for the abstract argumentation framework (AF).  Our model overcomes some intrinsic difficulties of the only random model of  directed graphs in the literature  that is relevant to  AFs, and makes it possible to study the typical-case complexity of AF instances in terms of  threshold behaviours and phase transitions.  We proved that  the probability for a random AF instance to  have a  stable/preferred extension goes through a sudden change (from 1 to 0) at the \r\nthreshold of the parameters of the new model D(n, p, q),  satisfying the equation 4q/((1 + q)(1+q)) = p.  We showed, empirically,  that in this new model, there is a clear easy-hard-easy pattern of hardness (for a typical backtracking-style exact solvers)  associated with the phase transition. Our empirical  studies indicated that instances from the new model at phase transitions are much harder than those from an Erdos-Renyi-style model with equal edge density.  In addition to being an analytically tractable model for  understanding  the interplay between problems structures and effectiveness of  (branching) heuristics  used in practical argumentation solvers,  the model can also be used to generate, in a systematic way,  non-trivial AF instances with controlled features to evaluate the performance of other AF solvers.","doi":"10.24963/ijcai.2017/71","url":"https://ijcai.org/proceedings/2017/71","pdf":"https://ijcai.org/proceedings/2017/0071.pdf","markdown":"https://ijcai.org/proceedings/2017/71.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/71","volume":{"slug":"2017","title":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2017","url":"https://ijcai.org/proceedings/2017/","year":2017,"location":"Melbourne, Australia","dates":"19-25 August 2017","editors":"Carles Sierra","isbn":"978-0-9992411-0-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2017"},"section":"Combinatorial & Heuristic Search","track":"Main track","number":71,"pages":{"first":503,"last":509},"keywords":["Knowledge Representation, Reasoning, and Logic: Computational models of Argument","Combinatorial & Heuristic Search: Combinatorial search/optimisation","Combinatorial & Heuristic Search: Evaluation and Analysis","Combinatorial & Heuristic Search: Heuristic Search"],"videos":[],"references":[{"position":1,"raw":"[Achlioptas and Peres, 2003] D. 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